Calculate gear modulus from pitch diameter and tooth count, or from outside diameter for standard metric spur gears. Enter teeth and diameter in mm or in to get modulus in mm and the related diameter.
Assumptions & Formulas
– Gear Modulus (m): Pitch Diameter (d) / Number of Teeth (z)
– Modulus from OD: Outside Diameter (da) / (Number of Teeth + 2)
Definitions & Constraints:
– Gear Modulus: The unit of size that indicates how big or small a gear is. Meshing gears must have the identical modulus.
– Physical Validity: A functional gear must have an exact, whole-number integer for its tooth count.
– Standard Gear Profile: Calculations involving Outside Diameter (da) assume a standard, unmodified gear profile with no profile shift (Addendum = 1m).
This tool calculates gear modulus from pitch diameter and tooth count, or from outside diameter and tooth count for standard metric spur gears. Diameter inputs accept mm or inches. Gear modulus is returned in mm, and the tool also returns the related secondary diameter.
Formula Used in This Gear Modulus Calculator
The tool relies on two distinct formulas depending on the calculation mode you select.
For the primary mode using pitch diameter, the formula is: $$m = \frac{d}{z}$$
Where $m$ is the gear modulus, $d$ is the pitch diameter, and $z$ is the number of teeth.
For the secondary mode using outside diameter, the formula is: $$m = \frac{da}{z + 2}$$
Where $da$ is the outside diameter. This formula strictly assumes a standard metric spur gear profile.
Formula and mode mapping
| Calculator mode | Formula used | Required inputs | Main result | Secondary result |
|---|---|---|---|---|
| Modulus from Pitch Diameter | $$m = d / z$$ | Pitch diameter, number of teeth | Gear modulus (mm) | Outside diameter |
| Modulus from Outside Diameter | $$m = da / (z + 2)$$ | Outside diameter, number of teeth | Gear modulus (mm) | Pitch diameter |
Inputs and Units
The calculator accepts the following inputs. You can enter diameter values in either millimeters (mm) or inches (in).
Inputs, outputs, units, and constraints
| Field | Type | Unit handling | Notes |
|---|---|---|---|
| Number of teeth ($z$) | Input | Whole number only | Must be at least 1 |
| Pitch diameter ($d$) | Input | mm or in | Used only in pitch-diameter mode |
| Outside diameter ($da$) | Input | mm or in | Used only in outside-diameter mode |
| Gear modulus ($m$) | Output | mm | Always returned in metric module |
| Calculated outside diameter | Output | mm or in | Returned in pitch-diameter mode |
| Calculated pitch diameter | Output | mm or in | Returned in outside-diameter mode |
Results This Calculator Returns
When you run a calculation, the primary result is always the gear modulus ($m$) expressed in millimeters. This is the standard metric unit defining tooth size.
Depending on your chosen input mode, the tool also returns a secondary measurement. If you calculate using pitch diameter, the tool outputs the corresponding outside diameter. If you calculate using outside diameter, it outputs the expected pitch diameter. You can switch these secondary diameter results between millimeters and inches.
How to Use the Calculator
To find the modulus of your gear, follow these steps:
- Select your calculation goal from the dropdown menu based on the diameter you know.
- Enter the number of teeth on the gear. This must be a whole number of at least 1.
- Enter your known diameter (either pitch or outside) and select your preferred unit.
- The tool instantly displays the calculated gear modulus in millimeters, alongside the complementary diameter value.
Modulus from Pitch Diameter vs Modulus from Outside Diameter
Using pitch diameter is the direct method for finding gear modulus. Because modulus is defined mathematically as the ratio of pitch diameter to the number of teeth, this method applies universally across different gear profiles.
Using outside diameter is valid only for standard, unmodified metric spur gears. It will yield incorrect modulus values if the gear has been modified or uses a non-standard profile shift.
Assumptions and Limitations
The main limitation applies to the outside diameter mode. The formula $m = da / (z + 2)$ assumes a standard gear profile where the addendum equals one modulus. It does not account for profile shifts, unequal addendums, or specialized gear geometries.
Additionally, the tool enforces physical reality by requiring the tooth count to be an exact integer. Partial teeth cannot exist on a functional gear, so the calculator will flag any non-whole number inputs as invalid.
FAQ
What is the formula for gear modulus?
Gear modulus is calculated as pitch diameter divided by number of teeth: $$m = d / z$$.
Can I calculate gear modulus from outside diameter?
Yes, but only under the assumption of a standard metric spur gear with no profile shift, using $$m = da / (z + 2)$$. That is a secondary mode in this tool and is based on specific gear assumptions, not the universal definition of module.
Is gear modulus always in millimeters?
For this tool, yes. The calculator allows pitch diameter and outside diameter to be entered in mm or inches, but the modulus result itself is returned in mm.
What inputs do I need to use this calculator?
You need the number of teeth plus either the pitch diameter to calculate modulus directly, or the outside diameter to calculate modulus for a standard metric spur gear.
Why does the calculator require whole-number teeth?
Because a physical gear must have an integer tooth count. The tool validates tooth count as a whole number input before calculating modulus to ensure the math reflects a real component.
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